1. Field of the Invention
The present invention relates generally to the field of computer simulation and prediction and more specifically to using a computer system and method for compensating dies used in stamping metal parts.
2. Related Art
A major factor in the success of a car company (or any company) is the ability to quickly roll out new models. The lead time required to develop a new car, from the initial designs to production line readiness, has over the years been reduced to approximately three years from well over five years in the recent past. In such a large scale development, there are many parts and processes that must be developed simultaneously in order for a car to be ready for production.
The design and perfection of the tools used for stamping of the metal parts, i.e. the body and chassis of a vehicle, remain the single longest lead time tasks of the entire development process. It requires approximately one year to develop and refine the dies for stamping of the body and chassis. This is largely because making a die that will create parts having the exact dimensions desired is a trial and error process requiring years of experience and craftsmanship. This is especially true with the use of lighter and more elastic materials that are gaining popularity in the quest for more fuel efficient and cleaner burning vehicles. The stamping of aluminum and other high tensile steel increasingly used in the production of vehicles is even more complicated than in the past.
Metal parts stamped in a die are subject to a phenomena known as springback. Springback is an elastic deformation which occurs at the end of a sheet metal stamping process, as the stamped part is removed from the stamping tools. Springback has the effect of changing the part's finished shape so that it no longer matches the shape of the tools. If this shape deviation is large, it can cause difficulty during a subsequent assembly process, or cause twisting in the assembled part. Accordingly, it is important to produce parts whose finished shape closely matches the designed surface. Usually corrections to compensate for springback are made by modifying the shape of the stamping tools (dies).
The design of these modifications, or die compensation, is a complex process. Two commonly used methods are the trial-and-error and spring-forward methods. The trial-and-error method predicts die modifications based on engineering experience. Usually many years of die-shop experience are necessary before an engineer can successfully guess how to change the dies. The trial-and-error method is also very time consuming: fabrication of a modified die set usually takes months of time. In addition, several trial-and-error corrections are frequently required before adequately compensated parts are obtained. Accordingly, the trial-and-error process is very expensive, often requiring over one million dollars to make a die which produces “good” parts. When new materials are used or when a new design is adopted, previous experience cannot be applied directly. These problems with the trial-and-error method can result in costs and lead-times which are out of control.
However, there are several major limitations to this process. First, the die has very limited access once it has been set up to stamp parts. It is quite cumbersome to separate a tool and die once it has been assembled to modify the die. Second, the dies are very complex, and altering one area of the die, or one bend, will affect another area, or a subsequent bend. The situation arises wherein a series of bends or other deformations each have springback errors compounding one after the other. In such complex parts, even the most skilled artisan has difficulty accommodating for springback. Third, even if the trial and error method could yield the perfect die shape to produce precisely dimensioned parts with the desired shape, the time and effort required to modify the die is tremendous and lengthens the overall development time of the vehicle. There is therefore a need for a predictive process and tool to create a die that will produce a part having exactly the desired dimensions in a shorter period of time, thus reducing the start to finish development time of new vehicles or other products.
Computer simulation has gained popularity in the stamping industry due to its speed and low cost, and it has been proven to be effective in prediction of formability and springback behaviors. However, to date no effective simulation method has been found to compensate the die based on the springback prediction.
The finite element method is a technique for obtaining approximate numerical solutions to boundary value problems which predict the response of physical systems subjected to external loads. The finite element method is described in detail by Thomas J. R. Hughes in “The Finite Element Method” (1987), published by Prentice-Hall, Inc., New Jersey, which is incorporated herein by this reference in its entirety. One common use of the finite element method is in the field of solid mechanics where it is used to analyze structural problems such as the formation of stamped sheet metal parts or the springback of stamped sheet metal parts. The equations describing the physical event of interest are generally overly complex to be solved exactly.
The finite element method is a technique where the geometry of the analyzed structure is approximated as a set of points in space. The points, which are referred to as nodes, are connected together to form finite elements.
The finite element method can be used to run two or three dimensional simulations. In a two-dimensional (2D) simulation the elements are areas. In a three-dimensional (3D) simulation the elements are volumes. All of the simulations illustrated in this example are 3D simulations. The elements are therefore three dimensional volumes. However, for ease of illustration and explanation cross sections are used to illustrate the invention. The elements and nodes form a mesh or grid, and these terms are used interchangeably throughout this application. Additionally, the elements are shown as cubes or rectangles, however other geometric shapes may be used.
In structural mechanics, the matrix equations describe the relationship between the stress and velocity fields and the acceleration field at a specific instant in time. To follow the deformation process, one needs to integrate the matrix equations in time. Due to non-linearities, an exact integration is generally not possible. A time discretization is necessary and one usually relies on a finite difference scheme to drive the solution forward in time. The matrix equations may be explicitly or implicitly integrated.
A well known simulation-based die compensation procedure is the spring-forward method. This method begins by performing a stamping simulation by finite element analysis (“FEA”), which provides information for the stamped part while it is still positioned in the closed dies. This information includes the geometry and material stress and strain data. The method then assumes that subsequent springback deformation will be driven by material stress, and that if the stress distribution through the material thickness is (artificially) reversed, the resulting springback deformation will also be in the reversed direction, as compared to the actual part. Based on this logic, the geometry which is obtained by springback analysis with reversed stress can be used to predict modifications to the dies. This method is very simple to apply, and it is the most popular numerical method. However, the method suffers from two major shortcomings which prohibit use in many practical applications.
The first major shortcoming of the spring-forward method is the so-called under-cut problem, where predicted die modifications lead to tools which are impossible to operate, as can be seen in FIG. 1B. Undercutting occurs when a tool wall or face in the compensated die geometry has a negative angle in relation to the stroke direction (the line of action in which the tools move during the punch and die closing process.) This creates interference between the punch and die as the tools close. Undercutting problems occur when compensating parts that have steep walls.
The second shortcoming of the spring-forward method is an issue of accuracy. Since the method can be applied only once, an unsatisfactory prediction of compensated geometry means that the method fails.
An additional difficulty in simulation-based springback compensation procedures used to date arises from the complexity of the die surfaces. Engineers typically make modifications to the original tool surface data using CAD software, then generate the FEA model again using the new CAD surfaces. This procedure is time consuming, and it is typically only applied to certain local areas of the tools. Accordingly, it is very difficult, if not impossible, to make a global modification to the die design based on the numerical predictions.